A281551 Prime numbers p such that the decimal representation of its Elias gamma code is also a prime.

3, 23, 41, 47, 59, 89, 101, 149, 179, 227, 317, 347, 353, 383, 389, 479, 503, 599, 821, 887, 929, 977, 1019, 1109, 1229, 1283, 1319, 1511, 1571, 1619, 1667, 1709, 1733, 1787, 1847, 1889, 1907, 1913, 1931, 2207, 2309, 2333, 2357, 2399, 2417, 2459, 2609, 2753, 2789, 2909, 2963, 2999, 3203, 3257, 3299

Offset

1,1

Links

Indranil Ghosh, Table of n, a(n) for n = 1..2014

Example

59 is in the sequence because the decimal representation of its Elias gamma code is 2011 and both 59 and 2011 are prime numbers.

Prog

(Python)
import math
from sympy import isprime
def unary(n):
....return "1"*(n-1)+"0"
def elias_gamma(n):
....if n ==1:
........return "1"
....k=int(math.log(n, 2))
....fp=unary(1+k)    #fp is the first part
....sp=n-2**(k)      #sp is the second part
....nb=k             #nb is the number of bits used to store sp in binary
....sp=bin(sp)[2:]
....if len(sp)<nb:
........sp=("0"*(nb-len(sp)))+sp
....return int(fp+sp, 2)
i=1
j=1
while j<=2014:
....if isprime(i)==True and isprime(elias_gamma(i))==True:
........print str(j)+" "+str(i)
........j+=1
....i+=1

Crossrefs

Cf. A000040, A171885 (decimal representation of Elias gamma code), A281149, A281316.

Sequence in context: A370601 A116893 A106066 * A167216 A309935 A212396

Adjacent sequences: A281548 A281549 A281550 * A281552 A281553 A281554

Keyword

nonn,base

Author

Indranil Ghosh, Jan 24 2017

Status

approved